Table 1 Causal assessment approach

Strength of association

Our scoping review of causal assessment found a range of effect sizes that were considered strong (e.g. RR > 1.20 and RR > 5.0). For GRADE, a strong association is an RR between 2–5 while a very strong is an RR greater than 5 [53]. We will extract the effect sizes from studies that conditioned upon individual income and, when synthesized, will note if it is considered “strong” according to GRADE. However, we will consider those alongside any information on residual confounding (i.e. the likelihood that confounding effects remain after conditioning), unmeasured confounding or evidence of over-adjusting such that the effect size is underestimated (see Table 4 for list of confounding variables).

Cohort and cross-sectional studies with multilevel modelling

1. Rather than focus on whether an effect size falls above a specific size, we will prioritize evidence that residual confounding and/or unmeasured confounding accounted for (including measure and assessment of the E-value, i.e. the minimum observed association that would unlikely be explained by a confounding variable [54]).

Consistency

Our scoping review found that reviews applying Bradford Hill viewpoints and considering consistency often aimed to understand if effect estimates were consistent across populations, settings or study designs. However, we will apply the principles of a realist review that focus on explaining why effect sizes may be similar or differ rather than determining if they are consistent. We will account for transportability (i.e. to what extent can causal effect in one context be applied to another) and what factors that undermine transportability help explain statistical heterogeneity across studies. If necessary, we will use DAGs to illustrate our assumptions about what factors (such as studies from the US) undermine transportability and how.

Cohort and cross-sectional studies with multilevel modelling

Natural experiments

1. Explanations for differences in effect sizes (articulated in a DAG) (see Table 4 for possible explanations).

2. Evidence that effect estimates are consistent across different settings and populations (especially if there is evidence that bias in these studies have been addressed).

Temporality

Evaluating a relationship’s temporality (i.e. if the exposure under study came before the outcome under study) involves assessing the evidence for reverse causation. Thus, longitudinal data are required to understand if a relationship between income inequality and health is observed even after conditioning upon individual health prior to changes in income inequality.

Cohort studies with multilevel modelling

Natural experiments

1. Health outcomes happened after income inequality change.

Specificity

We do not anticipate a lot of evidence to support a specific (i.e. one-to-one) relationship between income inequality and individual health. However, if we identify studies that look at falsification outcomes or exposures (i.e. variables associated with the confounding variable but not with the exposure or outcome under study, respectively), these will strengthen our certainty of a causal relationship. We will use DAGs to articulate our assumptions of falsification outcomes or exposures.

Cohort and cross-sectional studies with multilevel modelling

1. Evidence confounding variables were adequately conditioned upon using falsification outcome/exposures.

Dose-response

Evidence of a dose-response relationship may not be as useful in causal assessment as is commonly assumed [52], particularly if the impact of confounding variables is not considered alongside a dose-response gradient (as is the case with the strength of association). Because of this, we will only evaluate dose-response if we can identify studies that have taken confounding by individual-level income into account.

Cohort and cross-sectional studies with multilevel modelling

1. Evidence of a dose-response relationship within studies that have accounted for individual-level income.

Plausibility

Our scoping review found that many reviews considered a relationship plausible if a credible mechanism could be identified (though what constitutes as “credible” was not clarified). There are two well-known mechanisms explaining the relationship between income inequality and individual health: (1) psychosocial factors and (2) neo-material factors. While it is beyond the scope of the SR to determine which of these mechanisms is most plausible, we will note any empirical evidence that does examine mechanisms and narratively synthesize their findings.

Cohort and cross-sectional studies with multilevel modelling

Natural experiments

1. Empirical evidence (if any) that explains the mechanism by which income inequality causes individual health, to be synthesized narratively.

Experiment

Experimental evidence is considered amongst the most important for causal inference. We will consider natural experiments (multilevel and ecological cohort studies) to assess experimental support of causality. Two reviews from our scoping review used the MRC guidance on natural experiments to compare findings from observational data using different analytical methods and study designs to account for bias and emulate randomized studies. We will similarly compare the findings of studies using different methods.

Natural experiment

1. Evidence of an effect from natural experiment studies which better account for confounding than traditional observational studies.

2. Consistent findings from natural experiment studies using different methodological approaches.